Forcing Axioms, the Uniformization and the Basis Property

Abstract

We show that there are models of MA where the boldface ${\Sigma }_3^1$-uniformization property holds. Further we show that BPFA and the assertion ${\aleph }_1$ is accessible to reals outright implies that the boldface ${\Sigma }_3^1$-uniformization property is true.

31 pages

References in corpus (1)

• The Consistency of the ${\mathbf{\Sigma }}_3^1$-Separation Property

Cited by in corpus (2)

• $\mathsf{MA}(\mathcal{I}$) and a Failure of Separation on the third Level
• The global ${\Sigma }_{n+1}^1$-Uniformization Property and $\mathsf{BPFA}$